William Pratt

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.
G. K. Chesterton

The title page of Arithmeticall Jewell of William Pratt from 1617
The title page of Arithmeticall Jewell of William Pratt

A simple calculating device with the fancy name Arithmetical Jewell was designed by William Pratt in the middle 1610s, and described in the book of the same name (The Arithmeticall Jewell: or the use of a small Table Whereby is speedily wrought, as well all Arithmetical workes in whole Numbers, as all fractional operations, without fraction or reduction. Invented by William Pratt. Published by his Maiesties privilege, granted to the inventor, under the Great Seale of England), published in 1617 in London.

William Pratt, in association with John Harpur and Jeremy Drury, received a patent (privilege) on 27 March 1616, for the sole making of a table for casting accounts. The patent was for making a device “by which all questions arithmetical may be resolved without the use of pen or compters [counters]”. On 4 April 1616, the three men obtained a privilege for printing a book explaining an “instrument or table for cyfering and casting of accomptes”. Soon thereafter, the partners fell out, and published competing manuals of instruction: Harpur entered his in the Stationers’ Register on 8 March 1617, and Pratt on 21 June 1617.

The Arithmetical Jewell of Pratt is an instrument with a flat grid of semi-circular, rotating brass wedges, devised to facilitate addition, subtraction, multiplication, division, and the extraction of roots.

William Pratt was a mathematical practitioner and a member of the active circle of London’s mathematical teachers, close to the famous Gresham College, where the logarithms of Napier were popularized at that time.

The drawing of Arithmeticall Jewell of William Pratt from 1617
The drawing of Arithmetical Jewell of William Pratt from his book

Pratt’s device was nothing more than a rudimentary mechanical reconfiguration of the conventional reckoning technique: a portable, fancier, and gentlemanly adaptation of the century-old techniques of calculation like plume (manual calculations) and jetons of the abacus. With the exception here that you did not need paper to inscribe, for instance, the carry-over numbers of an addition; one could instead, using a small metallic stylus, “inscribe” them on the instrument’s appropriate sectors of brass. The reckoning method, nonetheless, was precisely the same as the plume and jetons.

The Arithmetical Jewell comprises two ivory-faced wooden tablets, with dimensions 122 mm x 65 mm x 5 mm each, put in tooled leather binding, 5″ x 3″, with a brass stylus 5 inches long. The weight of the device is only 0.14 kg. One tablet (below in the picture) has 14 columns, each with small brass parallel sectors, made from brass (copper, zinc alloy). The other has seven pairs of columns for laying out astronomical fractions to the base 60. Numbers are put in by moving the flags to reveal dots. Sums are then worked out with a pen and paper.

The Arithmeticall Jewell of William Pratt (© National Museums Scotland)
The Arithmetical Jewell of William Pratt (© National Museums Scotland)

There is a later account for Arithmetical Jewell by the English antiquary, natural philosopher, and writer John Aubrey (1626–1697):
Dr Pell told me, that one Jeremiah Grinken [a mathematical instrument maker] frequented Mr Gunters Lectures at Gresham College: He used an Instrument called a Mathematicall Jewell, by which he did speedily performe all Operations in Arithmeticke, without writing any figures, by little sectors of brasse [or some semi-circles] that did turn every one of them upon a Center. The Doctor has the booke… he told me, he thought his name is [William] Pratt.

Arithmetical Jewel in Science Museum Group Collection
The Arithmetical Jewell of William Pratt (© Science Museum Group Collection, https://collection.sciencemuseumgroup.org.uk/)

Jorge Luis Borges

I had found my religion: nothing seemed more important to me than a book. I saw the library as a temple.
Jean-Paul Sartre

Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo (24 August 1899 – 14 June 1986)

In 1939 the famous Argentine writer and librarian Jorge Luis Borges published in Buenos Aires an essay entitled La bibliotheca total (The Total Library), describing his fantasy of an all-encompassing archive or universal library.

A universal library is supposed to contain all existing information, all books, all works (regardless of format), or even all possible works. The Great Library of Alexandria is generally regarded as the first library approaching universality, in the classical sense, i.e containing all existing at the moment knowledge. It is estimated that at one time, this library contained between 30 and 70 percent of all works in existence. Universal libraries are often assumed to have a complete set of useful features (such as finding aids, translation tools, alternative formats, etc.)

As a phrase, the “universal library” can be traced back to 1545, when the Swiss scientist Conrad Gessner (1515-1565) published his Bibliotheca universalis. At the end of the 19th century, with the development of technologies, machines, and human imagination, appeared the idea of the device of a library which is universal in the sense that it not only contains all existing written works, but all possible written works. This idea appeared in Kurd Lasswitz’s 1901 story “The Universal Library” (Die Universalbibliothek), and was later developed by Borges.

In 1941, Borges enhanced his idea in the short story “The Library of Babel” (La biblioteca de Babel), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format and character set.

Borges’ story of a universe in the form of a library, or an imaginary universal library, has been viewed as a fictional or philosophical predictor of characteristics and criticisms of the Internet.

The narrator of “The Library of Babel” describes how his universe consists of an endless expanse of interlocking hexagonal rooms, each of which contains the bare necessities for human survival—and four walls of bookshelves. Though the order and content of the books are random and apparently completely meaningless, the inhabitants believe that the books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks). Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books. The narrator notes that the library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages. Conversely, for many of the texts some language could be devised that would make it readable with any of a vast number of different contents.

Despite — indeed, because of — this glut of information, all books are totally useless to the reader, leaving the librarians in a state of suicidal despair. However, Borges speculates on the existence of the Crimson Hexagon, containing a book that contains the log of all the other books; the librarian who reads it is akin to God.

Now, it seems we have already the device, which can create the Universal Library, and this is the computer. We still have not provided this device with the tools (intellect in the form of software, and some hardware resources) needed for the creation of this library, but sometime or another, this will happen.

Caroline Winter

Once made equal to man, the woman becomes his superior.

On 12 April 1859, a certain mysterious person, named C. Winter, of Piqua, from the county of Miami and the State of Ohio, received the 3-page US patent №23637 for Improved Adding-Machine, which was the fourth in the USA keyboard adder, after the machines of Parmelee, Castle and Nutz, and seventh in the world, after the machines of White, Torchi, and Schwilgué.

What makes this simple adding machine (in fact, a single column adding device. i.e. suitable for adding columns of numbers) a remarkable one is the fact, that (according to my personal investigation) its constructor is a woman, thus this machine is the first and the only mechanical calculator, devised by a woman. This remarkable lady was Caroline Winter from Piqua, a small town on the Great Miami River in southwest Ohio, developed along with the Miami and Erie Canal construction between 1825 and 1845.

Patent drawing of Caroline Winter's machine
Patent drawing of Caroline Winter’s machine (US patent No. 23637)

Almost nothing is known about the inventor of this machine—Caroline Winter. She was mentioned in the business directories for Piqua in 1859-60 and 1860-61 as the owner of a general store in the town. There is a tombstone in the Piqua’s Cedar Hill Cemetery of Caroline Winters, born in 1816, died on 8 Jan 1899 in Lima, Allen County, Ohio, at the home of her daughter—Amelia (Winters) Stein (1848-1932).

No doubt, Caroline Winter devised this machine to facilitate the tedious calculations in her store and trade business, as it is specified in the patent “It will be perceived that by the use of this machine figures may be added rapidly and always with perfect correctness.” Interestingly, the witnesses of her patent—Augustin Thoma and John B. Larger probably also significantly contributed to the creation of her machine. Note: Both of them were emigrants from Germany, as it was a large part of Piqua’s population in the middle of the 19th century. Caroline Winter was most probably also an emigrant from Germany because, in the United States Index to Passenger Arrivals, we can find two records (from 1833 and 1835) for women named Caroline Winter arriving in the USA from Germany.

John B. (Baptiste) Larger was a wealthy Piqua merchant (b. 1828 in Fellering, Departement du Haut-Rhin, Alsace, France), who unfortunately get killed young, when in early 1862 volunteered 32nd Regiment of Ohio Infantry to take part in Civil War, and was shot by a sniper in May 1862, while in camp.

Augustin (August, Augustus) Thoma (b. 3 Aug 1819 in Kappel (Lenzkirch), Baden, Germany, d. 30 Dec 1899 in Piqua, OH) was the founder of a successful jeweler’s business in Piqua (est. 1838), which was conducted by his descendants and survived up to 2010. He landed in New York at the age of 13 in 1832, served as an apprentice to a watchmaker, learned the trade, and in 1838 moved to Piqua to found his own jewelry business. Admittedly, Thoma was not only a good jeweler and merchant, but also a skillful instrument maker, and civic leader. He is a holder of three US patents—for a Jewelers Tool (pat. №67462 from 1867-08-06), for a Watch Jeweling Tool (№70049 from 1867-10-22), and for a Watch Maker Tool (№120618 from 1871-11-07), so we could easily imagine, that he was somehow involved in the construction of the Winter’s machine. Interestingly, Thoma had a daughter, named Caroline.

Winter's Keyboard Adder
Front view of the machine of Winter (© 2009 by Auction Team Breker, Koeln, Germany, www.breker.com)

In contrast to the first US keyboard calculating machines (these of Parmelee and Castle), the machine of Caroline Winter survived to the present, in the form of the Original U.S. Patent Model (up to 1880, the Patent Office required inventors to submit a model with their patent application). At the beginning of our century, the device was a property of Auction Team Breker, Koeln, Germany (see the photos below) and was restored and sold in an auction in 2009 for $46480 to Arithmeum Museum in Bonn, Germany (I guess Auction Team Breker could eventually get a much better price if they knew my assumption that this is the first (and only) mechanical calculator, devised by a woman 🙂 Arithmeum recently uploaded a 3D animated video made by a student of Computer Science, showing the functionality of the machine in detail and also giving an impression of its operation and aesthetics (see Arithmeum video on Winter’s machine).

The size of the machine is 27 x 22 x 25 cm. The box is made from oak, with ivory key taps and two dial faces on the plate on top of the registers. The base part of the internal calculating mechanism is the big ratchet wheel (marked with K on the patent drawing), which is provided with 100 teeth, a smaller ratchet wheel (n, for counting hundreds), bevel-wheels j and i, pawls s and z, cord o, and pulley P. The dial plate on top of the box has two dials: a big dial B, divided into 100 divisions, and a smaller dial for counting hundreds C, which is within the big dial, and is divided into 6 divisions, thus the calculating capacity of the machine is up to 699.

Winter's adding machine 1859 rear view
Rear view of the machine of Winter (© 2009 by Auction Team Breker, Cologne, Germany, www.breker.com)

The device has a resetting mechanism, presented by the lever (marked with c), which has its fulcrum at c’, slotted to embrace the shaft h, having a groove around it at the point of contact with the lever. d represents a spring secured to lever c, which serves to raise it again after being depressed.

The adding device of Caroline Winter doesn’t have a tens carry mechanism, and in fact, it doesn’t need it, because the smaller ratchet wheel (counting hundreds), rotates simultaneously with (and proportionally to) the bigger ratchet wheel (counting 1-99). However, when adding multidigit numbers, tens carry operations must be done manually, as it is described in the patent application.

Winter machine’s use of an elementary switching latch mechanism is characteristic since this mechanism had only been used in very few calculating machines before, for example, those made by Jean-Baptiste Schwilgué.

Blaise Pascal

I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is — oh dear! I shall never get to twenty at that rate!
Alice in Wonderland, by Lewis Carroll

Blaise Pascal
Blaise Pascal (1623-1662)

The Roulette ou Roue Paschaline (celebrated as Pascaline in France and abroad) of the great french scientist Blaise Pascal was for more than three centuries considered the first mechanical calculator in the world, as the Rechenuhr of Wilhelm Schickard was not widely known until the late 1950s. Pascal most probably didn’t know anything about Schickard’s machine. It is more likely Pascal to have read the Annus Positionum Mathematicarum, or Problemata (courses covering geometry, arithmetic, and optics) of Dutch Jesuit mathematician Jan Ciermans (1602-1648), who mentioned in his courses, that there is a method with rotuli (normally rolls of parchment for writing upon, but could also intend the more modern diminutive for rota i.e. little wheels) with pointers, which enables multiplication and division to be done with a little twist, so the calculation is shown without error.

In 1639 Étienne Pascal, the father of Blaise Pascal was appointed by the Cardinal de Richelieu as Commissaire député par sa Majesté en la Haute Normandie (financial assistant to the intendant Claude de Paris) in Rouen, capital of the Normandy province. Étienne Pascal arrived in the city of Rouen in January 1640. He was a meticulous, forthright, and honest man, and spent a considerable amount of his time completing arithmetic calculations for taxes. The task of calculating enormous amounts of numbers in millions of deniers, sols, and livres necessitated ultimately the help of his son Blaise and one of his cousins’ sons, Florin Perrier (1605-1672), who would soon marry Blaise’s sister Gilberte.

Étienne was buried with work and he and his helpers were often up until two or three o’clock in the morning, figuring and refiguring the ever-rising tax levies. They used initially only manual calculations and an abacus (counting boards), but in 1642 the Blaise started to design a calculating machine. The first variant of the machine was ready the next year, and the young genius continued his work on improving his calculating machine.

In his later pamphlet (Advis necessaire) Pascal asserted: …For the rest, if at any time you have thought of the invention of machines, I can readily persuade you that the form of the instrument, in the state in which it is at present, is not the first attempt that I have made on that subject. I began my project with a machine very different from this both in material and in form, which (although it would have pleased many) did not give me entire satisfaction. The result was that in altering it gradually I unknowingly made a second type, in which I still found inconveniences to which I would not agree. In order to find a remedy, I have devised a third, which works by springs and which is very simple in construction. It is that one which, as I have just said, I have operated many times, at the request of many persons, and which is still in perfect condition. Nevertheless, in constantly perfecting it, I have found reasons to change it, and finally recognizing in all these reasons, whether of difficulty of operation, or in the roughness of its movements, or in the disposition to get out of order too easily by weather or by transportation, I have had the patience to make as many as fifty models, wholly different, some of wood, some of ivory and ebony, and others of copper, before having arrived at the accomplishment of this machine which I now make known. Although it is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before, I assure you that all the jarring that it receives in transportation, however far, will not disarrange it.

The first several copies (certainly made by a local clockmaker in Rouen, it was a time when clocks and clockwork were celebrated, with even the Universe being considered, at least metaphorically, as being a form of clockwork) of the machine didn’t satisfy the inventor. Meanwhile, in 1643, it happened an event, which almost manage to give up Pascal from the machine. A clockmaker from Rouen dared, (according to the words of the offended inventor, who named no name—whether he knew it is unknown), to make a beautiful, but absolutely useless for work copy of the machine. Let’s look again at how is describing this event Pascal himself in his pamphlet (Advis necessaire):
…Dear reader, I have good reason to give you this last advice, after having seen with my own eyes a wrong production of my idea by a workman of the city of Rouen, a clockmaker by profession, who, from a simple description which had been given him of my first model, which I had made some months previously, had the presumption, to undertake to make another; and what is more, by another type of movement. Since the good man has no other talent than that of handling his tools skillfully and has no knowledge of geometry and mechanics (although he is very skillful in his art and also very industrious in many things which are not related to it), he made only a useless piece, apparently true, polished and well filed on the outside, but so wholly imperfect on the inside that it was of no use. Because of its novelty alone, it was not without value to those who did not understand about it; and, notwithstanding all these essential defects which trial shows, it found in the same city a place in a collector’s cabinet which is filled with many other rare and curious pieces. The appearance of that small abortion displeased me to the last degree and so cooled the ardor with which I had worked to the accomplishment of my model, that I at once discharged all my workmen, resolved to give up entirely my enterprise because of the just apprehension that many others would feel a similar boldness and that the false copies which they would produce of this new idea would only ruin its value at its beginning and its usefulness to the public. But, some time afterward, Monseigneur le Chancelier, having deigned to examine my first model and to give testimony of the regard which he held for that invention, commanded me to perfect it. In order to eliminate the fear which held me back for some time, it pleased him to check the evil at its root, and to prevent the course it could take in prejudicing my reputation and inconveniencing the public. This was shown in the kindness that he did in granting me an unusual privilege, and which stamped out with their birth all those illegitimate abortions which might be produced by others than by the legitimate alliance of the theory with art.

Later on, however, friends of Pascal presented to the Chancellor of France, Pierre Seguier (1588–1672), a prototype of the calculating machine. Seguier admired the invention and encouraged Pascal to resume the development. In 1645 Pascal wrote a dedicatory letter at the beginning of his pamphlet (the above-mentioned Advis necessaire) describing the machine (actually advertising the machine, as almost nothing is mentioned about its construction and operation) (see the letter and the pamphlet of Pascal), and donated a copy of the machine to the Chancellor (still preserved in CNAM, Paris). The text concluded that the machine could be seen in operation and purchased at the residence of Prof. Gilles de Roberval (Roberval was a friend of Étienne Pascal). This is the only preserved description of the device from the inventor.
The Chancellor Seguier continued to support Pascal and on 22 May 1649, by royal decree, signed by Louis XIV of France, Pascal received a patent (or privilege as it then was called) on the arithmetical machine, according to which the main invention and movement are this, that every wheel and axis, moving to the 10 digits, will force the next to move to 1 digit and it is prohibited to make copies not only of the machine of Pascal, but also of any other calculating machine, without permission of Pascal. It is prohibited for foreigners to sell such machines in France, even if they are manufactured abroad. The violators of the privilege will have to pay a penalty of 3 thousand livres (see the Privilege of Pascal).
The privilege again (as the Advise) mentions that Pascal has already produced fifty somewhat different prototypes. Moreover, the patent was awarded gratis and did not specify an expiration time, which was rather an unusual affair. It seems Pascal was an authentic favorite of the french crown 🙂

It seems later Pascal wanted to manufacture his machines as a full-scale business enterprise, but it proved too costly, and he didn’t manage to make money from this privilege. It’s not known how many machines were sold but the total was probably no more than ten or fifteen. Price may have been the main issue here, though accounts vary significantly, from the Jesuit mathematician François’s 100 livres to Tallemant de Réaux’s 400 livres and Balthasar Gerbier’s 500 livres (let’s mention, that 100 livres were enough to keep a seventeenth-century Frenchman in modest comfort for a year).

Pascal continued to experiment, constructing a lot of variants of the machine (later on called the Pascaline or Pascalene). He worked so hard on this machine, it is said, that his mind was disturbed (avoir latête démontée) for the next three years. According to his sister Gilberte, the young inventor’s exhaustion did not come from the labor he put into designing the machine, but rather in trying to make the Rouen artisans understand what it was all about.

Pascal decided to test the reliability of the machine, sending a copy on a long journey with carriage (from Rouen to Clermont and back, some one thousand kilometers) and the machine returned in perfect condition. Later he wrote: “Although [the Pascaline] is composed of many different small parts, as you can see, at the same time it is so solid that, after the experience of which I have spoken before of [‘carrying the instrument over more than two hundred and fifty leagues of road, without its showing any damage’], I assure that the jarring that it receives in transportation, however far, will not disarrange it.

Actually, the mechanism for tens carry is not very reliable and the machine has to be in a position, near to horizontal, in order to work reliably, and sometimes, a hit to the box can cause unwanted carry to be performed.

The Pascaline soon become well-known in France and abroad. The first public description was in 1652, in the newspaper Muse Historique. The machine was demonstrated to the public in Paris. Pierre de Ferval, a family friend and a mathematics professor at the Royal College of France, agreed to demonstrate the device to prospective customers in his apartment at the College Maitre Gervais every Saturday morning and afternoon. Pascal went to work writing advertising flyers for the invention and asked a friend, the poet Charles Vion Dalibray, to compose a publicity sonnet. The Polish queen Marie Louise de Gonzague, a high-ranking and keen patron of sciences, asked to buy two copies (her secretary Pierre Des Noyers already had a copy, and Polish monarchs were so fascinated by the device, that they wanted to buy two more). Another fan of science, Swedish queen Christina desired a copy to be granted to her. Pascal satisfied their desire (the device for queen Christina was sent together with a short manual), but soon after this lost his interest and abandoned his occasions with the calculation machine until the end of his short life.

A Pascaline from 1652
A Pascaline from 1652 (© Musée des Arts et Métiers, Paris)

Of some 50 constructed Pascalines, only 8-9 survived to the present day and can be seen in private or museum collections (4 in CNAM, Paris, 2 in a museum in Clermont, and several in private collections, e.g. in IBM).

The first copies of the machine were with five digital positions. Later on, Pascal manufactured machines with 6, 8, and even 10 digital positions. Some of the machines are entirely decimal (i.e. the scales are divided into 10 parts), and others are destined for monetary calculations and have scales with 12 and 20 parts (according to french monetary units: 1 sol = 12 deniers, 1 livre = 20 sols).

The dimensions of the brass box of the machine (for 8 digital positions variant) are 35.1/12.8/8.8 cm. The input wheels are divided by 10, 12, or 20 spokes, depending on the scale. The spokes are used for rotating the wheels by means of a pin or stylus. The stylus rotates the wheel until it gets to an unmovable stop, fixed to the lower part of the lid. The result can be seen in the row of windows in the upper part, where is placed a plate, which can be moved upwards and downwards, allowing to be seen the upper or lower row of digits, used for addition or subtraction.

Let’s examine the principle of action of the mechanism, using the lower sketch.

A sketch of the calculating mechanism of Pascalene
A sketch of the calculating mechanism of Pascalene

The input wheels (used for entering numbers) are smooth wheels, across which periphery are made openings. Counter-wheels are crown-wheels, i.e. they have openings with attached pins across the periphery.

The movement is transferred from the input wheel (marked with N in the sketch), which can be rotated by the operator by means of a stylus, over the counter, which consists of four crown-wheels (marked with B1, B2, B3, and B4), pinion-wheel (K), and mechanism for tens carry (C), to the digital drum (I), which digits can be seen in the windows of the lid.

The tens carry mechanism (called by Pascal sautoir), works in this way:
On the counter-wheel of the junior digital positions (B1) are mounted two pins (C1), which during the rotating of the wheel around its axis (A1) will engage the teeth of the fork (M), placed on the edge of the 2-legs rod (D1). This rod can be rotated around the axis (A2) of the senior digital position, and the fork has a tongue (E) with a spring. When during the rotating of the axis (A1) the wheel (B1) reaches the position, according to the digit 6, then pins (C1) will engage with the teeth of the fork, and at the moment, when the wheel moves from 9 to 0, then the fork will slide off from the engagement and will drop down, pushing the tongue. It will push the counter wheel (B2) of the senior position one step forward (i.e. will rotate it together with the axis (A2) to the appropriate angle. The rod (L), which has a special tooth, will serve as a stop, and will prevent the rotating of the wheel (B1) during the raising of the fork. The tens carry mechanism of Pascal has an advantage, compared e.g. to this of Schickard’s Calculating Clock, because it is needed only a small force for transferring the motion between adjacent wheels. This advantage, however, is paid for by some shortcomings—during the carrying is produced a noise, and if the box is hit, may occur unwanted carrying.

The wheels of the calculating mechanism are rotating only in one direction and there are no intermediate wheels provided (designated to reverse the direction of the rotation). This means, that the machine can work only as an adding device, and subtraction must be done by means of an arithmetical operation, known as a complement to 9. This inconvenience can be avoided by adding additional intermediate gear-wheels in the mechanism, but Pascal, as well as all the next inventors of calculating machines (Leibniz, Lepine, Leupold, etc.), didn’t want to complicate the mechanism and didn’t provide such a possibility.

The rotating of the wheels is transferred via the mechanism to the digital cylinders, which can be seen in the windows (see the photo below).

A view to the digital cylinders of Pascaline
A view to the digital cylinders of Pascaline

On the surface of cylinders are inscribed 2 rows of digits in this way, that the pairs are complemented to 9, for example, if the upper digit is 1, the lower is 8. On the lid is mounted a plate (marked with 2 in the lower sketch), which can be moved upwards and downwards and by means of this plate, the upper row of digits must be shown during the subtraction, while the lower one—is during the addition. If we rotate the wheels, we will notice that the digits of the lower row are changing in ascending order (from 0 to 9), while the digits of the upper row are changing in descending order (from 9 to 0).

Zeroing of the mechanism can be done by rotating of the wheels by means of the stylus in such a way, that between the two starting spokes (marked on the wheel) to be seen 9 (see the lower sketch). At this moment the digits of the lower row will be 0, while the upper digits will be 9 (or 12 or 20, for sols and deniers) (see the lower sketch). The manuscript Usage de la machine (this is the earliest known manuscript for Pascaline, from the 18th century. The first part of this document is a manual for an accountant and describes how to perform addition, subtraction, multiplication, and division.) gives the following method:
“Before starting a calculus, you shift the sliding cover that lays over the display windows toward the edge of the machine. Then you have to set the marked spokes in order to read “0” on all the drums. This is done by setting the stylus in between the spokes that are marked with white paper and by turning the wheel until the needle stops it. This brings for each wheel the highest digit the drum can have, that is to say, “9” for all the wheels devoted to the “Livres”, “19” on the “sols” wheel, and “11” on the “deniers” wheel. Then you turn the last wheel on the right of only one position […] afterward all the drums will display “0”.”

Zeroing of the mechanism of Pascaline
Zeroing of the mechanism of Pascaline

An instruction for work with the machine from Pascal didn’t survive to the present day, so different sources described different ways of manipulation. I will describe a way, which is optimal as a number of operations, needed for performing calculations. To use this way, however, the operator must know the multiplication table (during the multiplication operation), and be able to determine a complement to 9 for digits (for division and subtraction). This is an easy task even for 8 years old children now, but not for the men of the 17th century. Of course, the calculations can be done without following the two upper-mentioned requirements, but it will be necessary more attention and additional movements of the wheels.

First, let’s make an addition, for example, 64 + 83. We have to put the stylus between the spokes of the units wheels, against 4, and to rotate the wheel to the stop. In the lower row of windows (the upper was hidden by the plate) we will see 4. Then we rotate the wheels of the tens in the same way to 6. Then we have to enter the second addend, 83, and we will see the result, 147, meanwhile, one carry will be performed.

The subtraction will be a little more difficult and will require not only rotating but some mental work. Let’s make, for example, 182–93.

After zeroing the mechanism (to see 000 in the lower windows), the plate of the windows must be moved to the lower position, and at this moment in the windows can be seen the number 999. Then the minuend is entered as a complement to 9, i.e. the units-wheel is rotated for 7, the tens-wheel for 1, and the hundreds-wheel to 8 (the complement to 9 of 182 is 817). As the upper row of digits actually is moved to descending order, thus we have made a subtraction 999-817 and the result is 182 (see the lower sketch).

Subtraction with the Pascaline (first phase)
Subtraction with the Pascaline (first phase)

Then must be entered the subtrahend (93), making a subtraction 182–93 (during rotating of the wheels two carries will happen—during the entering of the units (3), the units wheel will come to 9, and a carry to the tens-wheel wheel will be done, moving the tens-wheel to 7; then during the entering of 9 to the tens-wheel, it will be rotated to 8, and a carry will be transferred to the hundreds-wheel, making it to show 0). So, we have the right result 182–93=089 (see the lower sketch).

Subtraction with the Pascaline (second phase)
Subtraction with the Pascaline (second phase)

It wasn’t that difficult, but the operator must be able to determine the complement to 9 of a number.

To be able to use the fastest way for multiplication, the operator must know (or use) a multiplication table. Let’s make the multiplication 24 x 38. First, we have to multiply (mentally or looking at the table) units of the multiplicand to the units of the multiplier (8 x 4 = 32) and enter the result 32 in the mechanism (see the lower sketch).

Multiplication with the Pascaline (first phase)
Multiplication with the Pascaline (first phase)

Then we have to multiply units of the multiplier to the tens of the multiplicand (8 x 2 =16), but to enter the result (16) not in the right-most digital positions (for units and tens), but in the next (the positions for tens and hundreds). This we will have the result 192 (32 + 160) (see the lower sketch).

Multiplication with the Pascaline (second phase)
Multiplication with the Pascaline (second phase)

Then we have to repeat the same operation for the multiplication of the units of the multiplicand to the tens of the multiplier (3 x 4 =12) and for the multiplication of the tens of the multiplier to the tens of the multiplicand (3 x 2 = 6), entering the intermediate results into wheels of tens and hundreds (12), and into the hundreds and thousands (06). We have the right result (912) (see the lower sketch).

Multiplication with the Pascaline (third phase)
Multiplication with the Pascaline (third phase)

The division with the Pascaline can be done in a way, similar to the manual division of the numbers—first, we have to separate the dividend into 2 parts (according to the value of the divisor). Then we have to perform consecutive subtractions of the divisor from the selected part of the dividend until the remainder will become smaller than the part. At this moment we have to write down the number of subtractions, this will be the first digit of the result. Then we have to attach to the remainder (if any) 1 or more digits from the remained part of the dividend and start again the consecutive subtractions until we receive the second digit of the result and to continue this operation again and again until the last digit of the dividend will be used. In the end, we will have the remainder of the division in the windows, while the result will be written.

It’s quite obvious, that the work with the Pascaline is not very easy, but the machine is completely usable for simple calculations.

Some people at the time almost suggest Pascal was in possession of some kind of magical powers during his work on Pascaline. e.g. in Entretien avec M. de Sacy: It was common knowledge that [Pascal] seemed able to animate copper, and to give to brass the power of thought. Little unthinking wheels, each rimmed with then ten digits, were so arranged by him that they could give accounts even to the most reasonable persons, and he could in a sense make dumb machines speak.

Pierre Petit (1617–1687)—a French scholar and an inventor of a tool with Napier’s rods wrote: I find that since the invention of logarithms and rabdology, nothing of significance occurred regarding the practice of numbers other than Monsieur Pascal’s instrument. It is a device truly invented with as much success and speculation as his author has intelligence and knowledge. It consists, however, in a number of wheels, springs, and movements, and one needs the head and hands of a good clockmaker to understand how it works and to manufacture it, as well as the skills and knowledge of a good arithmetician to operate it. [For all these reasons], one fears that its use will never become widespread and that instead of being employed in financial bureaux and regional administrations to calculate taxes, or in merchant offices to compute their rules of discount and company, [the machine] will be stored in cabinets and libraries, there to be admired.

Admittedly, not all impressions from Pascal’s contemporaries were positive. Some were unfavorable, such as the October 1648 letter of the English gentleman traveler Balthasar Gerbier to Samuel Hartlib. Gerbier came upon Pascaline not long after a model in wood was finished, and thought it resembled something invented in England 30 years earlier. (Gerbier most likely meant William Pratt’s Arithmetical Jewel from 1616, a simple calculating instrument, that was nothing more than a variant of the common abacus). Gerbier though found many problems with Pascaline.

First, its user had to be knowledgeable in arithmetic, which ran contrary to Pascal’s rhetorical stance. Multiplications and divisions were complicated and it even took two Pascalines to make a simple rule of three. Gerbier also found Pascaline rather big (two feet in length, 9 inches broad), heavy, difficult to move, expensive (50 pistoles, or 500 lives), and useless to anyone who would like to learn the art of arithmetic. In other words, Gerbier did not admire this mechanical contraption supposed to “think” by itself. He ended his letter to Hartlib quoting a former ruler of Netherlands: Infine a Rare Invention farre saught, and deare baught: putt them jn the Storre house was the old Prince of Orange wont to saye and lett us proceede on the ordinary readdy way.

Pascaline was described in many other sources also, e.g. in the 18th century books of Jean Gaffin Gallon—Machines et inventions approuvées par l’Academie Royale des Sciences, depuis son établissment jusqu’a présent; avec leur description (see description of Pascaline from Gallon).

Jacques de Vaucanson

My second machine, or automaton, is a duck… The duck stretches out its neck to take corn out of your hand; it swallows it, digests it, and discharges it digested by the usual passage.
Jacques Vaucanson, letter to Abbe´ Desfontaines, 1738

Jacques de Vaucanson
Jacques de Vaucanson (1709-1782)

Jacques de Vaucanson (1709-1782) was a great French engineer and one of the significant inventors of the 18th century, who is primarily credited with creating the world’s first “true” robots in the early 1730s, as well as for creating the first completely automated loom, and the first all-metal lathe in late 1740s.

Jacques Vaucanson was the tenth child of a poor glove-maker from Grenoble. As a little boy, Jacques quickly revealed his talent by fixing the watches and clock mechanisms of his neighbors, constructing a clock and a small automaton-priests that duplicated a few of the ecclesiastical offices. Therefore, his family initially wanted Jacques to become a clockmaker but was forced in 1715 to send him to study at the Jesuit school in Grenoble (now Lycée Stendhal). In 1725 Vaucanson took orders and joined the Les Ordre des Minimes in Lyon. In 1728 Vaucanson decided to leave the monastery to devote himself to his mechanical interests and departed to Paris, where he remained until 1731. There he studied medicine and anatomy at the Jardin du Roi, being encouraged and supported by the Parisian financier Samuel Bernard (1651-1739), one of the wealthiest men of his time.

In 1731 Vaucanson left Paris for Rouen, where he met the famous surgeon and anatomist Claude-Nicolas Le Cat (1700-1768), whose own interests in replicating human anatomical forms and movements likely stimulated Vaucanson to begin work on his first automaton. Later Vaucanson met another famous French surgeon and economist, François Quesnay (1694-1774), who also encouraged him to create artificial creatures in order to put in evidence most of the human or animal biological functions. Thus the young Vaucanson decided to further develop his knowledge in anatomy by making living anatomies.

In 1732 Vaucanson traveled around France exhibiting his first automaton which he described as “a self-moving physical machine containing many automata, which imitate the natural functions of several animals by the action of fire, air, and water.”

In 1733, Vaucanson signed a contract to build and exhibit another automaton with Jean Colvée (1696-1750), a man of the cloth whose interests included chemistry, natural history, geography, and various business ventures. In 1736 however, having squandered funds supplied by Colvée, Vaucanson signed an agreement with a Parisian gentleman, Jean Marguin, to build an automated flute player in exchange for financial support—Marguin would retain one-third ownership of the completed automaton and receive half the money taken in when it was exhibited. Thus Vaucanson devoted himself to his first android musician, The Flute Player, which he finished in 1737, and demonstrated to the French Academie in April 1738. Later in 1738, he opened an exhibition to the public first at the fair of Saint-Germain, then in a rented hall, the grand salle des quatre saisons at the Hôtel de Longueville in Paris, in which presented initially only The Flute Player, but at the end of the year added two other automata, the Duck and the Tambourine Player.

Vaucanson 3 Automata
The Flute Player, the Duck, and the Tambourine Player. From the prospectus of the 1738 exhibition of Vaucanson’s automata, Vaucanson, Le Mecanisme du fluteur automate.

Despite the substantial admission ticket (three livres, a week’s salary for a worker at that time), the exhibition was a triumph. In addition to making money, the three automata captured the fancy of Voltaire, who celebrated Vaucanson as Prometheus’s rival and persuaded Frederick the Great to invite their maker to join his court, but the inventor denied it, because Louis XV also supported him. When the visitors decreased Vaucanson started a triumphant wide tour through France, and then to Italy and England.

The Flute Player was a life-size (178 cm tall) figure of a shepherd, dressed in a savage, that played the transverse flute and had a repertoire of twelve songs (in the nearby image you can see the inner workings of Vaucanson’s flute player). The tune was played on a real instrument, a mechanism moves the lips and fingers of the player and pumps air through his mouth. The fingers are carved in wood with a piece of leather at the point where they cover the holes. The entire figure is made of wood with the exception of the arms which are made of cardboard.

The Flute Player was seated on a rock put on a pedestal, like a statue. The case, enclosing a large part of the weight engine mechanism, housed a wooden cylinder (56 cm in diameter and 83 cm in length), which turned on its axis. Covered with tiny protrusions, it sent impulses to fifteen levers, which controlled, by means of chains and strings, the output of the air supply, the movements of the lips, the tongue as well as the articulation of the fingers.

The flute player of Vaucanson
The Flute Player of Vaucanson

In the same 1738 Vaucanson presented The Flute Player to the French Academy of Science. For this occasion, he wrote a lengthy report—a dissertation entitled “Mechanism of the automaton flute player” (“Mécanisme du flûteur automate”), carefully describing how his automaton can play exactly like an alive person. These were the Academy’s conclusions: The Academy has heard the reading of a dissertation written by M. Jacques de Vaucanson. This dissertation included the description of a wooden statue playing the transverse flute, copied from the marble fauna of Coysevox. Twelve different tunes are played with a precision which merited the public attention, and to which many members of the Academy were witnesses. The Academy has judged that this machine was extremely ingenious; that the creator must have employed simple and new means, both to give the necessary movements to the fingers of this figure and to modify the wind that enters the flute by increasing or diminishing the speed according to the different sounds, by varying the position of the lips, by moving a valve which gives the functions of a tongue, and, at last, by imitating with art all that the human being is obliged to do. Moreover, M. Jacques de Vaucanson’s dissertation had all the clarity and precision of which this machine is capable, which proves both the intelligence of the creator and his extensive knowledge of all the mechanical parts.

As we already mentioned, in the same 1738, Vaucanson created two additional automatons, The Tambourine Player and The Digesting Duck (Canard Digérateur), which is considered his masterpiece.

There is very little information on The Tambourine Player. The automaton stood on its pedestal, like The Flute Player. The Tambourine Player was a life-sized man dressed like a Provençal shepherd, who could play 20 different tunes on the flute of Provence (also called galoubet) with one hand, and on the tambourine with the other hand with all the precision and perfection of a skillful musician. It must have been equipped with a very complex mechanism, because it could play two different musical instruments and, according to Vaucanson, the galoubet was the “most unrewarding and inexact instrument that exists.” Besides, he made the following note: “A curious discovery about the building of this automaton is that the galoubet is one of the most tiring instruments for the chest because muscles must sometimes make an effort equivalent to 56 pounds…”.

The Digesting Duck was Vaucanson’s masterpiece, and it was a very remarkable machine for its time. Interestingly, in 1733, several years before Vaucanson, a similar automaton was presented to the Paris Academy of Sciences by a mechanician named Maillard. Maillard’s Cygne artificiel (artificial swan) sported a mechanical paddle wheel and gears to navigate through the water while turning its head from side to side, reproducing the motion of a swimming duck. The device was described in Gallon’s “Cygne artificiel,” Machines, 7 vols., from 1735.

The Digesting Duck of Vaucanson
The Digesting Duck of Vaucanson

Vaucanson’s Duck was made of gilded copper and had over 400 moving parts, and could quack, flap its wings, drink water, digest grain, and defecate like a living duck. Although Vaucanson’s duck supposedly demonstrated digestion accurately, his duck actually contained a hidden compartment of “digested food”, so that what the duck defecated was not the same as what it ate. Although such “frauds” were sometimes controversial, they were common enough because such scientific demonstrations were needed to entertain the wealthy and powerful to attract their patronage. Vaucanson is credited as having invented the world’s first flexible rubber tube while in the process of building the duck’s intestines. Thanks to the open structure of its abdomen, the audience could even follow the digestive process from the throat to the sphincter which ejected a sort of green gruel.

Vaucanson provided his own description of his duck: …a duck, in which I show the mechanism of the viscera employed in the functions of drinking, eating, and digestion; the way in which all the parts required for these actions function together is imitated precisely: the duck extends its neck to take the grain out of the hand, it swallows it, digests it and expels it completely digested through the usual channels; all the movements of the duck, which swallows precipitously and which works its throat still more quickly to pass the food into its stomach, are copied from nature; the food is digested in the stomach as it is in real animals, by dissolution and not by trituration, as a number of physicists have claimed it; but this is what I intend to demonstrate and show upon that occasion. The material digested in the stomach passes through tubes, as it does through the entrails in the animal, to the anus, where there is a sphincter to allow its release.
I do not claim that this digestion is perfect digestion, able to make blood and nourishing particles to nurture the animal; to reproach me for this, I think, would show bad grace. I only claim to imitate the mechanics of this action in three parts which are: firstly, swallowing the grain; secondly, macerating, cooking, or dissolving it; thirdly, expelling it in a markedly changed state.
However, the three acts needed means, and perhaps these means will deserve some attention from the persons who would demand more accuracy. They will see the expedients that we used to make the artificial duck take the grain, suck it up into its stomach, and there, in a little space, build a chemical laboratory, to break down the main integral parts from it, and make it go out with no limit, through some convolutions of pipes, at an all opposed end of its body.
I think that attentive people will understand the difficulty to make my automaton perform so many different movements; for instance, when it rises up onto its feet, and it steers its neck to the right and to the left. They will know all the changes of the different fulcrums; they will even see that what acted as a fulcrum for a mobile part, becomes then mobile on this part which becomes fixed itself. At last, they will discover an infinity of mechanical combinations.

At the time, mechanical creatures were somewhat of a fad in Europe, but most could be classified as toys, and de Vaucanson’s creations were recognized as being revolutionary in their mechanical life-like sophistication. In spite of the considerable success of his three automata, Vaucanson tired of them quickly and sold them in 1743 to some entrepreneurs from Lyon, who toured with them for nearly a decade, showing them throughout Europe. Admission was always charged at these exhibitions and the automata appear to have brought in considerable revenue. Unfortunately, none of this survived to the present time. The musician automatons were lost or destroyed at the beginning of the 19th century, while the duck burnt in a museum in Krakow, Poland in 1889. For nearly 40 years, however, until his death in 1782, Vaucanson worked on the plan to make “an automaton’s face which would closely imitate the animal processes by its movements: blood circulation, breathing, digestion, the set of muscles, tendons, nerves, and so far…”

In 1741 Vaucanson was appointed by Cardinal André-Hercule de Fleury, chief minister of Louis XV, as inspector of the manufacture of silk in France. He was charged with undertaking reforms in the silk manufacturing process because at the time, the French weaving industry had fallen behind that of England. In 1742 Vaucanson promoted wide-ranging changes for the automation of the weaving process. Between 1745 and 1750, he created the world’s first completely automated loom, drawing on the work of Basile Bouchon and Jean Falcon, who he probably knew from his life in Lyon in the 1720s. However, Vaucanson’s loom was not successful, his proposals were not well received by weavers, who pelted him with stones in the street and eventually lead to strikes and social unrest in Lyon.

A reconstruction of Vaucanson's loom (© CNAM, Paris)
A reconstruction of Vaucanson’s loom (© CNAM, Paris)

In the mechanism of Vaucanson’s loom, the hooks that were to lift the warp threads were selected by long pins or needles, which were pressed against a sheet of punched paper, that was draped around a perforated cylinder. Specifically, each hook passed at a right angle through an eyelet of a needle. When the cylinder was pressed against the array of needles, some of the needles, pressing against the solid paper, would move forward, which in turn would tilt the corresponding hooks. The hooks that were tilted would not be raised, so the warp threads that were snagged by those hooks would remain in place; however, the hooks that were not tilted, would be raised, and the warp threads that were snagged by those hooks would also be raised. By placing his mechanism above the loom, Vaucanson eliminated the complicated system of weights and cords (tail cords, pulley box, etc.) that had been used to select which warp threads were to be raised during weaving. Vaucanson also added a ratchet mechanism to advance the punched paper each time the cylinder was pushed against the row of hooks.

The idea behind the loom of Vaucanson was ingenious and technically sound, the prototypes also worked reasonably well. The problem, though, was that the metal cylinders were expensive and difficult to produce. Moreover, by their very nature, they could only be used for making images that involved regularly repeated designs. Obviously, by switching to new cylinders it is possible to produce designs of open-ended variety, but in practice, the switching over of cylinders proved too time-consuming and laborious. A few examples of the loom went into production, but it never really caught on and was soon discontinued.

Moreover, in 1741 Vaucanson commenced a project, to construct an automaton figure that simulated in its movements the animal functions, the circulation of the blood, respiration, digestion, the operation of muscles, tendons, nerves, etc. However, this was a too ambitious project. In 1762, he began to work on the more modest project of a machine, that would simulate just the circulation of the blood, using rubber tubes for veins. But this project, too, remained unrealized, because of inadequacies in contemporary rubber technology.

Jacques de Vaucanson was one of the significant inventors of the 18th century. In 1740 he demonstrated a clockwork-powered carriage. He is known as the builder of one of the first all-metal slide rest lathes (in 1750), the precursor of the machine tools that will be developed during the 19th century. He was also one of the first, who used rubber in his machines. In 1770 he developed the first western chain drive, which is used in silk reeling and throwing mills.

Biography of Jacques de Vaucanson

Jacques de Vaucanson (1709-1782)
Jacques de Vaucanson (1709-1782)

Born as Jacques Vocanson (the particle de was added to his name in 1746 when he was made a member of the Académie des Sciences) on 24 February 1709 in the French town of Grenoble, he was the tenth child of the poor glove-maker Jacques Vocanson, born in Toulouse, and his wife Dorothée La Croix.

From an early age, Jacques quickly revealed his talent by fixing the watches and clock mechanisms of his neighbors, constructing a clock and a small automaton-priests that duplicated a few of the ecclesiastical offices. Therefore, his family initially wanted Jacques to become a clock-maker but was forced in 1715 to send him to study at the Jesuit school in Grenoble (now Lycée Stendhal), then in Collège de Juilly from 1717 to 1722. In 1725, influenced by his mother, Vaucanson took orders and joined the Les Ordre des Minimes in Lyon.

There is an interesting legend for Vaucanson from this period: It seems despite his interest to follow a course of religious studies, Vaucanson retained his interest in mechanical devices, because in 1727, being just 18 years of age, he was given his own workshop in Lyon, and a grant from a nobleman to construct a set of machines. In the same 1727, there was a visit from one of the governing heads of Les Ordre des Minimes. Vaucanson decided to make some automata, which would serve dinner and clear the tables for the visiting politicians. However, one government official declared that he thought Vaucanson’s tendencies “profane”, and ordered that his workshop be destroyed.

Vaucanson's house, 51 rue de Charonne, 11th arrondissement, Paris
Vaucanson’s house, 51 rue de Charonne, 11th arrondissement, Paris, a photo from May 1889

Around 1730 a big influence on young Vaucanson appeared to apply Claude-Nicolas Le Cat (1700–1768), an eminent French surgeon and science communicator, who taught him anatomy, wherefore it became easier to construct devices that would mimic biological functions.

Jacques de Vaucanson married to Madeleine Rey on 8 August 1753, in Paris. They had one daughter, Angélique Victoire de Vaucanson (7 November 1753 – 15 August 1820).

Toward the end of his life, Vaucanson collected his own and others’ inventions in what became in 1794 the Conservatoire des Arts et Métiers (Conservatory of Arts and Trades) in Paris; it was there that Joseph-Marie Jacquard found his automatic loom.

Jacques de Vaucanson died aged 73 years old on 21 November 1782 in his house, 51 rue de Charonne, 11th arrondissement, Paris.

Luigi Torchi

Acknowledgement to my correspondent Mr. Silvio Hénin, Milan, Italy, for his pioneering work on Torchi’s calculating machine.
Georgi Dalakov

The machine of the Italian Luigi Torchi from Milan was the first full-keyboard/direct multiplication machine in the world, moreover, it was the first practical keyboard calculator, as the earlier key-driven adding machine, described by the English engineer James White, seems to remain only on paper. Some 40 years will be needed for the direct multiplication machine to be reinvented by the American Edmund Barbour in 1872.

In 19th century, in Milan operated the R.I. Istituto Lombardo Veneto di Scienze, Arti e Lettere (Royal Imperial Lombard-Venetian Institute of Sciences, Arts and Letters), founded by Napoleon in 1797. Among the initiatives of this body, there was the institution of the Premj d’Industria (Prizes for Industry), awarded every year to those entrepreneurs and firms that achieved distinction in their areas of activity. In 1834 the Golden Medal was awarded to the local carpenter Luigi Torchi for the invention and construction of a Macchina pei Conteggi (counting machine). In charge of the assignment were the mathematician Gabrio Piola and the astronomer Francesco Carlini.

The Acts of the Solemn Distribution of Prizes include:
A young carpenter named Louigi Torchi… with no more than a tincture in the science of numbers, driven only by the strength of his ingenuity, imagined and performed with the petty means that he had at his disposal, pieces of wood and iron wire, a species of that machine which will perform the arithmetic operations, which first imagined Pascal, and after him few other mechanical and mathematical disciples…

In the following years, the arithmetic machine enjoyed a high local reputation, to the point that Torchi’s name was listed among the “Italians distinguished in science, literature, and the arts”.

Francesco Carlini was so enthusiastic about Torchi’s machine to ask the Government for an appropriation to build a more reliable metal model for the activities of the Brera’s Astronomical Observatory. On 6 May 1840, the Government confirmed the authorization with the following letter: “The Government authorizes the direction of the Imperial Royal Observatory to build the machine for counting, imagined by the carpenter Torchi, for the amount of 1000 Lire.” Carlini summoned Torchi: “I invite you to meet me in order to take the concert and fix the price”. At this point the story seems to come to an end, every trace of the machine is lost and we do not know if Torchi replied to Carlini’s letter or ever accepted the proposal, but it seems the improved metal exemplar was never built.

Thirty-two years later, in 1872, the famous Italian astronomer Giovanni Schiaparelli (who first described the canals on Mars) examined what remained of Torchi’s machine and found it “lacking many pieces, almost all the front part containing the device for the preparation [the keyboard] and the reading of the results is missing”. Schiaparelli concluded that “the completion and repair require not only to examine the machine to get an idea of the nature of its mechanism but also a long and expensive work of a clever craftsman”.

The ingenuity of Luigi Torchi revealed itself in another instance. In 1835 he invented a horse-less cart, exploiting the energy of the water stream, that moved along the canal towing-path, dragging the barge. An experiment was performed in October 1835 in the presence of H. M. the Viceroy: the boat and the barge went along a 212 meters stretch in 13 minutes and 25 seconds (0.948 Km/h). For this achievement, in 1837 Torchi was awarded another prize by the Institute, the Silver Medal. The fame of this invention spread as far as France, as it can be read in an article in the Mémorial encyclopédique et progressif des connaissances. Another known to us invention of Torchi is an improved “pendulum level” from 1858.

Almost nothing has been published on the mechanism of Torchi’s calculator. Most of the sources available just praise the machine, e.g. in Piola and Carlini’s report of the award: “It [the machine] responds to the touch of the keys [performing] the first three arithmetical operations with such a rapidity that the most experienced [human] computer cannot match its speed”, and also “it is especially of great help when several multiplications should be carried out, where a factor remains constant, as for proportionate shares, to reduce weights and measures of one country into another’s and it is useful to relieve the painful work of the [human] computers of tables.”

Only two documents propose a more thorough description of Torchi’s calculator, perhaps both by the same author; one is the hand-written Report of the Award Committee, and the second is an article published in the journal “La Fama” in 1836, where we can find the description of the operations and the only known picture of the machine (see the sketch below). The Report of the Award Committee includes: This combination of a constant and a variable number within certain limits, can be obtained by toothed sprockets and it is amazing to observe their particular configuration and bizarre teeth pattern. In spite of the poverty of the descriptions, two important features strike the attention: it was a “full-keyboard calculator” and it performed multiplication “instantaneously”.

The calculating machine of Luiggi Torchi
The calculating machine of Luigi Torchi (© Biblioteca Braidense, Milan, Italy)

Unless the fortuitous discovery of other documents or, almost impossible, of the machine or of parts of it, we cannot draw any definitive conclusion on the principle of operation of the Torchi’s contrivance and its innovative value. The lack of information may be attributable to Torchi himself, who would not have allowed any accurate inspection of his calculator to avoid possible plagiarism. In those times a craftsman was hardly protected from copies and Torchi’s bent on secrecy seems thus understandable.

The latest documented news about Luigi Torchi is the 1858 article about the pendulum level, written by Angelo Parrocchetti and Schiaparelli’s notes of 1872. If in nearly forty years since the prize, nothing more was recorded about the calculating machine and its inventor, one should think of a serious reason.

Why was the metal prototype never built? We can imagine that maybe the calculator was not as reliable as the enthusiastic descriptions bring us to understand?! Or maybe Torchi himself was not self-confident enough to work with different technology and with greater precision, and yet he was a carpenter, while the experience of a watchmaker or a scientific instruments maker was more appropriate?! Or maybe, finally, the inventor claimed more than the promised 1000 Lire?!

What happened to the prototype of his calculator? We know that it was probably exhibited in the Palace of Science and Arts of Brera from 1834 to 1837. It was then brought back to Torchi’s workshop, to be found again at the Brera Palace in 1872, when it was examined by Schiaparelli. We can imagine that, by that time very damaged and built with perishable material, it did not survive longer.

Strangely, almost nothing is known about this remarkable inventor—Luigi Torchi, except that he was born in 1812 and worked at the southern borders of the city of Milan (he lived in Borgo San Gottardo n° 1023, a neighborhood in Milan) as a mill carpenter. Torchi probably died before 1872. The exact details of his death have not been found in the city archives in Milan, as well as those relating to his origins, so probably Torchi was born and died far from the Lombard capital.

1. S. Hénin, La macchina calcolatrice del falegname Luigi Torchi, PRISTEM Lettera Matematica, Luglio 2008
2. S. Hénin, Two Early Italian Key-driven Calculators, IEEE Annals of the History of Computing, 2010. n. 1

Jean-Baptiste Schwilgue

Acknowledgement to my correspondent Mr. Denis Roegel, Professor at Loria, France, for his important works on Schwilgué’s calculating machines.
Georgi Dalakov

Portrait of Jean-Baptiste Schwilgué
Jean-Baptiste Schwilgué (1776-1856)

In 1844 the French engineer Jean-Baptiste Schwilgué from Strasbourg, together with his son Charles-Maximilien, patented a key-driven calculating machine, which seems to be the third key-driven machine in the world, after these of James White and Luigi Torchi, but was certainly the first popular keyboard calculator. Similar machines will be invented and manufactured by many inventors in the next 60 years. Moreover, several years later Schwilgué devised a bigger specialized calculating machine.

Additionneur Schwilgué (Schwilgué’s Adder)

Before starting the creation of his calculating machines, Schwilgué made a number of preliminary studies years before, such as a design of the computus mechanism (Easter computation) in 1816, of which he built a prototype in 1821. This mechanism, whose whereabouts are now unknown, could compute Easter following the complex Gregorian rule. The astronomical part is unusually accurate: it indicates leap years, equinoxes, and much more astronomical data.

Schwilgué himself was trained as a clockmaker, but also became a professor of mathematics, weights and measures controller, and an industry man, whose particular focus was on improving scales. After the completion of his famous astronomical clock of Strasbourg Cathedral in the early 1840s and following a change in the French patent laws, Schwilgué, with or without his son, patented several inventions, including the above-mentioned small adding machine. This machine appeared in the 1846 catalog of Schwilgué’s tower clock company, but was most probably devised some 10 years ago, in the middle 1830s.

The key adder of Schwilgué, a device from 1846 ((© Historical Museum Strasbourg)
The key adder of Schwilgué, a device from 1846, carrying the Nr. 15 (© Historical Museum Strasbourg)

As of now, several copies of the machine are known: one is in a private collection (Boutry-Ungerer family), one (dated 1846) in the Strasbourg Historical Museum (the machine (see the upper image) is in a poor state and carries the Nr. 15), and one (dated 1851) is in the collections of the Swiss Federal Institute of Technology in Zurich (see the lower images).

The calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology)
The calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology)
A side view of the Schwilgué's machine in Zurich (Courtesy of the Swiss Federal Institute of Technology)
A side view of Schwilgué’s machine in Zurich (Courtesy of the Swiss Federal Institute of Technology)

Like other machines of this kind (so-called single-column adders), the device of Schwilgué was intended to add a single digit at a time, i.e. the unit column is entered first, then the tens, the hundreds, the thousands, and so on, certainly rather cumbersome task (as every partial sum had to be recorded on paper and the sum eventually performed), which greatly limits the usefulness of such devices.

The inside of calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
The inside of calculating machine of Schwilgué in Zurich (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
Under the top plate of calculating machine of Schwilgué (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)
Under the top plate of calculating machine of Schwilgué (Courtesy of the Swiss Federal Institute of Technology and Mr. Denis Roegel)

In closed status, the machine is a box with nine numbered keys, an opening showing two or three digits in two parts, and two knurled knobs. It is 25.5 cm long, 13.6 cm wide, and 9.5 cm tall (without the knobs), weight 3.3 kg. The inside of one of the machines is almost identical to the patent drawing (see the next figure).

The patent drawing of the calculating machine of Schwilgué
The patent drawing of the small calculating machine of Schwilgué

Schwilgué’s machine has three main functions: addition, carrying, and setting.

The upper figure shows figures I, II, III, and IV of Schwilgué’s patent. Figure IV shows how the keys operate. Each key can move downward by an amount corresponding to its value and moves the wheel G, but only when the key is released. (Schwilgué stated, however, that this can be changed, to work on key pressing). This wheel meshes with wheel H (horizontal in Figure III), and the unit wheel moves counterclockwise by as many digits as the pressed key. The unit wheel is the wheel on the right of Figure II. It contains each digit three times.

The units and tens wheels can be set using the knurled knobs, so that before an addition the openings would show 00. On the Zurich machine, resetting the wheels is made easier by pins located under the wheels. When the knobs are pushed downwards, R or U disengage, but the pins are put in the way of stops so that one merely has to turn the knobs until it is no longer possible.

It may seem surprising to see such an invention, long after more sophisticated calculating machines such as Thomas’s Arithmometre (1820), or even the Roth machine (1841). It must, however, be understood that Schwilgué’s machine was never meant as a general adding machine.

Schwilgué, who had obtained a number of patents since the 1820s, was no doubt well aware of Thomas’s machine and other general calculating machines. We know, for instance, that Schwilgué had a copy of the description of Roth’s machines, as well as a copy of a history of calculating instruments published in 1843 by Olivier. It is possible that these articles were an incentive for Schwilgué to build his calculating machine, or they may have been part of his research for his own machine.

Unlike that of the general-purpose calculating machines, Schwilgué’s purpose was to ease a particular operation, the hand checking of addition. In these cases, only small values were handled, and Schwilgué didn’t bother to build a machine with 10-digit inputs, although it could probably have been done with his carrying mechanism. Instead, Schwilgué could see that the existing machines, although powerful in principle, were of little use for everyday accounting. Schwilgué’s machine was designed to fill that gap by using keys to input numbers. Schwilgué could see their potential, even though he never claimed to have invented the keyboard, as keyboards already existed on musical instruments.

The calculating machine of Schwilgué has several other interesting features (some are mentioned only in the patent):
The one, that has already been mentioned, is the use of a clock escapement-like way of adding the carry, although Schwilgué never qualified it that way. This feature seems also present on Schilt’s machine.

The patent drawing also shows that the keyed figures are only taken into account when the keys are released. However, Schwilgué stated explicitly that both are possible, either upon pressing or upon release and that the patent covers both.

Schwilgué also mentioned an interesting feature which he called “tout ou rien” (all or nothing). Besides the name, which alludes to binary logic and may have been borrowed from Julien Le Roy in the context of repeating watches that had to ring all chimes or none, it was here an optional feature ensuring that a digit was only taken into account when the key had been completely pressed. However, according to Schwilgué, this was not really needed as one learned quickly to operate the machine and not to make mistakes. A similar safety measure was introduced as late as 1913 in the ill-fated E-model of the Comptometer of Dor Felt. On that, an automatic blocking device prevents errors and forces the operator to repeat pressing a key that was not adequately depressed.

Schwilgué’s Calculator of Sequences

It is known also, that in the middle 1840s Schwilgué constructed a bigger specialized calculating machine, a solid brass device with 36 result wheels, kept now in the collection of Historical Museum Strasbourg (see the lower photo). This machine was advertised at “300 to 400” francs in 1846 (about three months’ salary for a common laborer of the period), and at “400 to 500” francs in 1847, but it seems unlikely that any was sold because it was too specialized.

Schwilgué's Calculator of Sequences (© Historical Museum Strasbourg)
Schwilgué’s Calculator of Sequences (© Historical Museum Strasbourg)

This specialized machine had a single purpose—to calculate multiples of some value using additions, and on 12 digits (i.e. the machine works with 12-digit integers, and it computes their multiples in sequence). In the 1830s and 1840s Schwilgué made several gear-cutting machines, which position is given by angles at regular intervals. To be able to calculate the angles with a large accuracy, Schwilgué wanted to compute the fractions 1/p, 2/p, 3/p…, p/p on 12 places. Thus the output of the calculating machine (values were copied on paper) can be used as an input for the gear-cutting machine.

The machine is a weight-driven device with a modular design and includes 12 almost identical blocks (one for each place), a command arbor, and a command block. A crank is provided (normally not used), for rewinding the machine and clearing carries.

Once the machine is rewound, a detent is shifted and the mechanism does one addition, then stops. This operation is repeated until the machine is rewound. After each computation, the values are copied on paper.

The command block is similar to a striking clock with two 54-teeth wheels, a pinion of 9 leaves, a second wheel of 47 teeth, and a double threaded worm. The weight is attached to a string that is wound around a drum driving one of the 54 teeth wheels, and this wheel meshes with the second 54 teeth wheel, as well as with the pinion. The second 54 teeth wheel drives the command arbor. The pinion drives the second wheel and the worm which leads to a brake and an arm stopped by the detent. When the detent is released, the arm is freed and the mechanism turns, until the detent again meets a notch on the 54 teeth wheel of the command arbor. There is also a notch in the other 54 teeth wheel, and the two work together as in common striking clocks.

Schwilgué's bigger calculating machine (© Denis Roegel)
Schwilgué’s bigger calculating machine (© Denis Roegel)

When the command block is triggered, the 54 teeth wheels perform one turn and so does the command arbor. This arbor is tangent to the 12 blocks and carries 24 arms, organized helically, two per block. It is a natural consequence of the relative position of the blocks, of the arbor, and of the need to sequentialize the additions at each place: first the units, then the tens, etc. The arrangement of the computing blocks dictates the structure of the command arbor.

Each block displays three digits and the three sets of 12 digits represent three 12-digit numbers. One is a simple counter, and it will show 000000000000, 000000000001, 000000000002, etc. The other is a constant and will never change during an operation. It will for instance store a value such as 076923076923 for 1=13. The third one will merely show the multiples of the constant. There are therefore two independent, but synchronous, functions: the counter, and the multiple. These functions are synchronous so that one value (the counter) could serve as an entry to the second (the multiple). In the case of the counter, the machine has to add one to the units, and to propagate the carries. In the case of the constant, the constant must be added to the stored sum, and carries have to be propagated. Each of these two functions is obtained by two arms of the command arbor. One arm is for incrementing the counter, the other is for adding one digit of the constant to one digit of the sum.

The prototype of the machine was probably constructed in 1844, but the earliest known plans are from 1846. Later the machine seems to have slightly evolved and the above-mentioned device follows plans dated 1852.

Schwilgue’s bigger machine should be remembered as an exceptional example of his engineering genius and as a rare example of an early specialized calculator, full of subtle features.

Biography of Jean-Baptiste Schwilgué

Jean-Baptiste Schwilgué, portrait by Gabriel-Christophe Guérin from 1843
Jean-Baptiste Schwilgué, portrait by Gabriel-Christophe Guérin from 1843

Jean-Baptiste Sosime Schwilgue was born on 18 Dec. 1776 in Strasbourg, France, in a house located at the intersection of rue Brûlée and rue de la Comédie. He was the second son of the civil servant François-Antoine Schwilgue (1749-1815) and Jeanne Courteaux (1750-1784). François-Antoine was native from Thann in Grand Est (Schwilgue (or Schwilcke) family settled in Thann centuries ago), and came to Strasbourg to serve as valet de chambre in l’Intendance royale d’Alsace à Strasbourg. Jeanne Courteaux was native from de Solgne (Moselle). Jean-Baptiste had an elder brother, Charles Joseph Antoine, born on 10 Oct. 1774, who became a doctor and professor of medicine in Paris, but died only 33 years old on 7 Feb. 1808. His mother Jeanne also died young on 13 April 1784, when Jean-Baptiste was only 8, and his father married second time in June 1785 to Marie-Anne Kauffeisen (1746-1809).

As a boy, Jean-Baptiste showed great interest in mechanics, and with the help of the simplest tools available to him, he produced various machines and instruments, by which he made special improvements that he had conceived. He was very fond of looking at the Strasbourg Cathedral astronomical clock, made in the 1570s by Konrad Dasypodius (1532-1600), and often stood for hours before it, thinking about putting this highly sophisticated watch (which at the time was very badly or not at all functional anymore), again in the workable state.

In 1789, after the outbreak of the French Revolution, the father of Jean-Baptiste lost his position and moved from Strasbourg to Sélestat (Schlestadt), Alsace (he died there on 14 Feb. 1815), where Jean-Baptiste continued his studies, devoting himself, especially to mathematics. Besides his studies, he learned the art of watch-making, entering a watch-making shop as an apprentice.

Anne Marie Thérèse Hihn-Schwilgué
Anne Marie ‘Thérèse’ Hihn-Schwilgué

In 1796 Jean-Baptiste became self-employed and married Anne Marie “Thérèse” Hihn (1778-1851, see the nearby image), a daughter of the confectioner Charles Hihn and Thérèse Baldenberger, on 25 April in Sélestat.

Eight children, three boys and five girls, were born from this marriage: Marie Thérèse (1797-1848), Jean-Baptiste (1798-1855), Charles-Maximilien (1800-1861), Françoise (1802-1806), Louise (1804-1864), Adélaïde (Adèle) (1806-1850), Sébastien “Alexandre” (1811-1836), and Marie “Clémentine” Emilie (1812-1878).

In 1807 Jean-Baptiste was appointed official at the district’s office of Sélestat (he was the town clockmaker and verifier of weights and measurements), and also a professor of mathematics at the local college, which he retained until he moved to Strasbourg in 1827. In the meantime, he was always occupied with the Strasbourg astronomical clock, and around 1820 he invented a mechanical church calendar with a precise determination of the movable festivals according to the Gregorian. This church calendar, which he had carried out in a smaller model (15×20 cm), he brought to the French Academy of Sciences in 1821, and even presented it personally to King Louis XVIII.

The third astronomical clock of Strasbourg Cathedral
The third astronomical clock of Strasbourg Cathedral

The masterpiece of Schwilgué’s life was the third astronomical clock of Cathédrale Notre-Dame de Strasbourg. As early as 1827, Schwilgué had submitted to the city council of Strasbourg a report on the condition of the clock, together with three proposals on the repair of the same; the first two, while retaining certain parts of the old clock, and the third, for a completely new clock. But it was not until 1836, after lengthy negotiations, that the city council of Strasbourg came to a final decision on the restoration of the clock, and was only approved by the higher administrative authority at the beginning of 1838. As the agreement was signed in May 1838, in June, Schwilgué set to work on the new clock. Together with his son Charles and his apprentices and later partners—brothers Albert and Theodor Ungerer, he was able to finish this assignment in July 1842. On 2 October 1842, on the occasion of the 10th Congress of Sciences in France in Strasbourg, the clock was set in motion for the first time, and Schwilgué was congratulated on all sides for the great success of the work which he had undertaken. In November 1842, a large banquet was held in his honor, and on 31 December 1842, a grand feast with a solemn parade through the town to commemorate the fortunate prosperity of the work erected by Schwilgué.

In 1835 Schwilgue was appointed Knight of the Legion of Honour and in 1853 on a report of the Minister of Education and Religious Affairs he obtained the rank of Officer of the Legion of Honour.

Jean-Baptiste Sosime Schwilgue died 79 years old on 5 December 1856 in Strasbourg (see below the gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie “Thérèse” Hihn). His son Charles inherited his father in the workshop (and in 1857 wrote a book about his famous father, named Notice sur la vie, les travaux et les ouvrages de mon pere, J. B. Schwilgue), but in 1858 he was paralyzed by a stroke, and died three years later.

The gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie "Thérèse" Hihn in Strasbourg
The gravestone of Jean-Baptiste Schwilgué and his wife Anne Marie ‘Thérèse’ Hihn in Strasbourg

Denis Roegel: An Early (1844) Key-Driven Adding Machine, IEEE Annals of the History of Computing, vol. 30, №1, pp. 59-65, January-March 2008)

Dubois D. Parmelee

Каждый мечтает изменить мир, но никто не ставит целью изменить самого себя.
Лев Николаевич Толстой

In 1850 Dubois D. Parmelee, a 20-year-old student at New Paltz Academy (later the State University of New York), patented a calculator, which seems to be the fourth key-driven adding machine in the world (after the machines of James White, Luigi Torchi, and Jean-Baptiste Schwilgué), thus putting the foundation of the US key-driven calculating machines industry, which will become the leading in the world industry some 40 years later.

Parmelee was an inventive young man, who devised his Machine for Making Calculations in Figures while in the New Paltz Academy, driven probably by the need to facilitate the tedious mathematical calculations. Unfortunately, nothing except the patent application survived to the present, even the patent model was lost (for most of the 19th century, US Patent Office required inventors to submit a model with their patent applications. Inventors placed great importance on their models and viewed a well-executed model as the key element in obtaining a patent.)

Like other machines of this kind (so-called single-column adders), the device of Parmelee was intended to add a single digit at a time, i.e. the unit column is entered first, then the tens, the hundreds, the thousands, and so on, certainly a rather cumbersome task (as every partial sum had to be recorded on paper and the sum eventually performed), which greatly limits the usefulness of such devices.

The patent drawing of the machine of Parmelee
The patent drawing of the calculator of Dubois D. Parmelee

The calculator of Parmelee is a simple apparatus for making additions of long columns of figures by means of a movable index or register acted upon by keys of a fingerboard (keyboard). The device (see the lower patent drawing from US patent No. 7074) has nine keys, which are numbered from 1 to 9 and have increasing heights.

The motion from the keys is transferred to the stick (graduated rule) B in the back part. This stick has in his front part teeth, which are engaging with the two tongues m and k (see figure 2 from the patent drawing). The sidebar of the stick is graduated and numbered in such a way, that one tooth corresponds to one division. On pressing a key, lever E will raise the tongue k to so many divisions, according to the digit, written on the key. Then the lever will be returned to the starting position by means of the spring n. When entering the numbers (or when the stick is raised to the uppermost position), the operator can see the number in the sidebar and then pulls by means of the two ropes p the two tongues and the stick will fall down through the box to its stop ready to be again raised.

It seems that if the machine of Parmelee was ever used to add with, the operator would have to use a pussyfoot keystroke, otherwise, the numeral bar would overshoot and give a wrong result, as no provision was made to overcome the momentum, that could be given the numeral bar in an adding action.

In his patent description, Parmelee proposed some improvements, the most important one was to improve the visualization, including in the construction gear wheels and strips.

In August 1850 the calculator of Parmelee was presented in the American popular science magazine Scientific American (see the image below):

The calculator of Parmelee in August 03, 1850, issue of Scientific American magazine
The calculator of Parmelee, as presented in the 3 August 1850, issue of Scientific American magazine

Biography of Dubois D. Parmelee

Dubois (Du Bois) Duncombe Parmelee, a known at his time chemist and inventor, was born on 15 August 1829, in Redding, a small town in Fairfield County, Connecticut. He was the son of Ezra Parmelee and Mary Duncombe Parmelee. Ezra Parmelee (born 5 March 1796) descended from one of the area’s first colonial settlers, John Parmelee (1615-1690) from East Sussex, England, who arrived at New Haven in July 1639.

After attending a private school in Boston, Parmelee enrolled in New Paltz Academy (now the State University of New York at New Paltz), where he received in the second half of the 1850s a degree in medicine and chemistry. He never worked as a physician however but devoted his life primarily to experimental chemistry.

After his graduation, Parmelee worked in the rubber industry in Salem, Mass, (in the US Census 1860 records he is listed as Dubois D. Parmalee, chemist, 29 y.o., living in 2nd Ward of Salem) where he invented the cold process of manufacturing rubber and had a rubber business until the Goodyear invention ran out and rubber prices dropped. Around 1861 he settled in New York and was listed in the New York City directories of the period 1 May 1862, through 1 May 1873, as a chemist. Later Parmelee worked for New York Belting and Packing Co. as a consulting chemist and took part in producing the first aluminum in the USA.

Parmelee was one of the most active members of the American Institute of the City of New York and several exhibits of his inventions have been made there. He joined the American Institute in 1861, and he was listed as an annual member in the membership list of 1868, with his profession given as Practical Chemist.

Parmelee was a holder of quite a few patents, primarily in the fields of rubber manufacturing and implementation (pat. №№ US24401, US26551, US48993, US48993, US187302, US146092, etc.) It seems his most important invention was the suction socket for artificial limbs (U.S. Utility Patent No. 37637), some 80 years before it received general acceptance. Parmelee fastened a body socket to the limb with atmospheric pressure, thus being the first inventor to do so with satisfactory results.

Dubois Parmelee married Rosina (Benisia) Gloward (b. 1836) in New York City on 7 October 1857, but apparently, they had no children.

Dubois Duncombe Parmelee died of heart failure on 15 April 1897, in New York.

James White

Acknowledgement to my correspondent Mr. Denis Roegel, Professor at Loria, France, for his unveiling work on White’s adding machine.
Georgi Dalakov

In 1822, James White, an English civil engineer, and prolific inventor published a very interesting 394-page book with the long name A New Century of Inventions: Being Designs and Descriptions of One Hundred Machines, Relating to Arts, Manufactures, and Domestic Life. Remarkably, among the 100 machines, described by White, there is a unique adding machine, which is the first key-driven calculator in the world.

In the early 1820s, late in his life (in the preface White mentions his declining health and approaching mortality), he decided to publish most of (or at least the 100 implied in the title) his inventions. It was obviously a work of some importance, indicated by the names of eminent engineers, who subscribed to it, like Charles Babbage (the creator of Differential Engine and Analytical Engine, Bryan Donkin, Jacob Perkins, William Fairbairn, and others. The same year the book ran to a second edition, and even in our time it also has several reprints on paper and an Ebook version.

We don’t know when exactly White devised his amazing keyboard adder, but in any event, it was long before the next known at the moment keyboard calculators of Luigi Torchi (1834) and Jean-Baptiste Schwilgué (1844). Most probably White invented the machine while in France in the early 1800s (he lived in Paris from the end of 1792 until February 1815), where he had the opportunity to study the machines of some famous French inventors, kept in Paris museums (e.g. Musée des Arts et Métiers), like Pascaline of Blaise Pascal, automata of Jacques de Vaucanson, etc. Sure enough, Vaucanson was mentioned twice in the book, regarding his chaîne Vaucanson, which White planned to use in the endless geering chain of his calculator.

The title page of New Century of Inventions of James White
The title page of New Century of Inventions of James White, Manchester 1822

Obviously, James White was related to and greatly influenced by the prominent British statesman and scientist Charles Stanhope, who had a family seat in Chevening, Kent, where White lived in the early 1790s. Charles Mahon, 3rd Earl Stanhope, is the subject of another article in this humble site, describing his mechanical calculating devices and logic machine. James White mentioned Stanhope three times in his book, as my noble friend, and my noble Patron. In the description of the adding machine, there is a paragraph, referring to Stanhope:
I would just repeat, that I have not attempted here an arithmetical machine in general; but a Machine fit for the daily operations of the counting-house: by which to favour the thinking faculty, by easing it of this ungrateful and uncertain labour. Had I been thus minded, I could have gone further, in a road which has been already travelled by my noble friend the late Earl Stanhope, (then Lord Mahon) but I took a lower aim; intending in the words of Bacon—”to come home to men’s business and bosoms.”

The adding machine of White is a single-column adder (i.e. it was intended to add a single digit at a time, as the unit column is entered first, then the tens, the hundreds, the thousands, and so on, certainly a rather cumbersome task (as every partial sum had to be recorded on paper and the sum eventually performed), which greatly limits the usefulness of such devices.) with very interesting construction, which cannot be found in the later machines. The motion from keys to the calculating mechanism and result dial is transferred by means of a pulley, that presses on an endless gearing chain. The chain is pushed out of its regular circular path by the depression of a key. This action causes the result wheel to turn an amount equal to the length of the key being pushed (the “1” key being 1 unit long, the “2” key, 2 units, etc).

The principle of carrying is shown in Figure 3 (see the image of the first plate below). One wheel carries a pin that, when rotated, advances another wheel by one tooth. The position of the moving wheel is secured by the spring wafer ED.

This construction of the machine makes it possible to type in several digits at the same time. However, there is no way to ensure that the keys are pressed to the bottom, which is something that some later machines will be able to enforce, for instance, by adding the digits only upon the release of a key but not upon its pressing.

A very interesting detail of White’s calculator is a kind of “floating point” mechanism, in that the motion of wheel B (see figure 1 below) rotates the square shaft B G, on which lies a sliding wheel l. This wheel can be moved to the appropriate position, should we add units, tens, hundreds, and so on, or other units (e.g. monetary, like farthings, pence, shillings, and pounds), such as those in use at the time of White.

As White did not patent his adding machine, and no account from his contemporaries survived for this remarkable contrivance, we can assume that the device does not appear to have been anything except a paper design and even a working prototype has not been made.

Let’s see White’s detailed description and illustrations of his adding machine (an excerpt of his book, pages 343–348, and plates 42 and 43):

Or Machine to Cast up large Columns of Figures.

This Machine is not, generally, an arithmetical Machine. It points lower: and therefore promises more general utility. Though less comprehensive than machines which perform all the rules of arithmetic, it is thought capable of taking a prominent place in the counting-house, and there of effecting two useful purposes—to secure correctness; and thus, in many cases, to banish contention. It is represented in figs. 1, 2, 3, and 4 of Plate 42, and in figs. 3 and 4 of Plate 43.

There are two distinct classes of operations that may be noticed in this Machine: the one that does the addition, properly speaking; and the other that records it by figures, in the very terms of common arithmetic. The first operation is the adding: which is performed by means of an endless gearing chain, stretched round the wheels A B C D, (fig. 1) and over the two rows of smaller pulleys a b c d e f g h i; where, observe, that the chain is bent round the pulley A, merely to shorten the Machine, as otherwise the keys 1 2 3, &c. to 9, might have been placed in a straight line, and thus the bending of the chain have been avoided.

The chain, as before observed, geers in the wheels B and D, which both have ratchets to make them turn one way only. Now, the keys 1 2, &c. have pulleys at their lower ends, which press on the aforesaid chain more or less according to the number it is to produce, and the depth to which it is suffered to go by the bed on which the keys rest, when pressed down with the fingers. Thus, if the key 1 be pressed, as low as it can go, it will bend the chain enough to draw the wheel B round one tooth—which the catch E will secure, and which the wheel C will permit it to do by the spring F giving way. But when the key 1 is suffered to rise again, this spring F will tighten the chain by drawing it round the pulleys A and D, thus giving it a circulating motion, more or less rapid, according to the number of the key pressed. Thus, the key 5 would carry five teeth of the wheel B to the left; and the catch E would fix the wheel B in this new position: after which the spring T would tighten the chain in the same direction and manner as before. It is thus evident, that which-ever key is pressed down, a given number of teeth in the wheel B, will be taken and secured by the catch E; and, afterwards, the chain be again stretched by the spring F. It may be remarked, that, in the figure, all the keys are supposed pressed down: so as to turn the wheel B, a number of teeth equal to the sum of the digits 1, 2, 3—to 9. But this is merely supposed to shew the increasing deflexion of the chain, as the digits increase: for the fact can hardly ever occur. We draw from it, however, one piece of knowledge—which is, that should the eye, in computing, catch several numbers at once on the page, the fingers may impress them at once on the keys and chain; when the result will be the same as though performed in due succession.

Plate 42 of White's New Century of Inventions
Plate 42 of White’s New Century of Inventions

Thus then, the process of adding, is reduced to that of touching (and pressing as low as possible) a series of keys, which are marked with the names of the several digits, and each of which is sure to affect the result according to it’s real value: And this seems all that need be observed in the description of this process. It remains, however, to describe the 5th. figure, which is an elevation of the edge of the keyboard, intended to shew the manner in which the two rows of keys are combined and brought to a convenient distance, for the purpose of being easily fingered.

We now come to the other part of the subject—that of recording the several effects before-mentioned. The principle feature in this part, is the System of carrying, or transferring to a new place of figures, the results obtained at any given one. This operation depends on the effect we can produce by one wheel on another, placed near it, on the same pin; and on the possibility of affecting the second, much less than the first is affected: Thus, in fig. 3 and 4, (Plate 42,) if A be any tooth of one such wheel, placed out of the plane of the pinion B, it will, in turning, produce no effect upon that pinion: but if we drive a pin (a) into the tooth A, that pin will move the pinion B one tooth (and no more) every time this pin passes from a to b. And if we now place a second wheel (F) similar to A, at a small distance from it, so as to geer in all the teeth of the pinion B, this latter wheel will be turned a space equal to one tooth, every time the pin a passes the line of the centres of the wheel and pinion A B, (say from a to b.) It may be added, likewise, that this motion, of one tooth, is assured by the instrument shewn at E D, which is called in French a tout ou rien, (signifying all or nothing) and which, as soon as the given motion is half performed, is sure to effect the rest: and thus does this part of the process acquire, likewise, a great degree of certainty—if indeed, certainty admits of comparison.

It is then, easy to perceive, how this effect on the different places of figures is produced; and it is clear, that with the chain motion just described, it forms the basis of the whole Machine. There is, however, one other process to be mentioned, and as the 2nd. figure is before us, we shall now advert to it. In adding up large sums, we have sometimes to work on the tens, sometimes on the hundreds; which mutations are thus performed: The wheel B, (fig. 2) is the same as that B, fig. 1; and it turns the square shaft B G, on which the wheels k l slide. The wheel l is to our present purpose. It is now opposite the place of shillings; but by the slide m, it can be successively placed opposite pounds, tens, hundreds, &c. at pleasure: on either of which columns, therefore, we can operate by the chain first described—the wheel B being the common mover.

Plate 43 of White's New Century of Inventions
Plate 43 of White’s New Century of Inventions

We shall now turn to figs. 3 and 4 of Plate 43, which give another representation of the carrying-mechanism, adapted especially to the anomalous carriages of 4, 12, and 20, in reference to farthings, pence, shillings, and pounds, and then following the decuple ratio.

In fig. 3, k l represent the two acting wheels of the shaft B G, fig. 2; the latter dotted, as being placed behind the former; these wheels, however, are not our present object, but rather the carrying system before alluded to; and described separately, in fig. 3 of Plate 42. A, in figures 3 and 4 (of Plate 43) is the first wheel of this series. It has 12 teeth with three carriage-pins (or plates) a, which jog the carrying pinion B, at every passage of 4 teeth; thus shewing every penny that is accumulated by the farthings. This is so, because the farthings are marked on the teeth of this first wheel in this order-1, 2, 3, 0; 1, 2, 3, &c. and it is in passing from 3 to 0, that this wheel, by the carriage-pinion B, jogs forward the pence wheel C one tooth: But this pence wheel is divided into 12 numbers, from 0 to 11; and has on it only one carrying-pin (or plate) b; so that, here, there is no effect produced on the third wheel D, until 12 pence have been brought to this second wheel C, by the first, or farthing wheel A. Now, this third wheel D, is marked, on it’s twenty teeth, with the figures 0 to 19, and makes, therefore, one revolution, then only, when there have been twenty shillings impressed upon it by twenty jogs of the carriage-pin b, in the second wheel C. But when this wheel D has made one whole revolution, it’s single carriage-pin c, acting on the small carriage-pinion, like that c d, (but not shewn) jogs forward, by one tooth, the wheel E, which expresses pounds; and having two carriage-pins e f, turns the wheel called tens of pounds, one tooth for every half turn of this wheel E: and as, on all the succeeding wheels, to the left from E–(see fig. 2, Plate 42) there are two sets of digits up to 10, and two carriage-pins; the decuple ratio now continues without any change: and thus can we cast up sums consisting of pounds, shillings, pence, and farthings, expressing the results, in a row of figures, exactly as they would be written by an accountant. The opening, through which they would appear, being shewn in fig. 1, at the point w, corresponding with the line x y of fig. 2 in the same Plate.

I shall only remark, further, that the figures 3 and 4 in Plate 43, are of the natural size, founded, indeed, on the use of a chain that I think too large; being, in a word, the real chain de Vaucanson, mentioned in a former article: and that the figures of Plate 42 are made to half these dimensions, in order to bring them into a convenient compass on the Plate.

I would just repeat, that I have not attempted here an arithmetical machine in general; but a Machine fit for the daily operations of the counting-house: by which to favour the thinking faculty, by easing it of this ungrateful and uncertain labour. Had I been thus minded, I could have gone further, in a road which has been already travelled by my noble friend the late Earl Stanhope, (then Lord Mahon) but I took a lower aim; intending in the words of Bacon—”to come home to men’s business and bosoms.”

End of excerpt from book A New Century of Inventions of James White

Biography of James White

Most of the scarce information, available for the life of James White, comes from biographical statements in his only book A New Century of Inventions.

James White was born in 1762 in Cirencester, Gloucestershire (located some 150 km northwest of London), at that time a thriving market town, at the center of a network of turnpike roads with easy access to markets for its produce of grain and wool. Interestingly, no record of his birth is to be found in the Church Baptismal Register there, so his parents may have been nonconformists (or even (judging by his too-common English name and surname, and lack of information about his parents) that he was born out of wedlock son of a nobleman, who wanted to remain in secret).

White’s father gave free rein to his son’s early predilection for mechanics as is illustrated by the fact that when the boy was only about eight years of age and still at school he invented quite an ingenious mouse trap. As James White stated:
Should any reader then enquire what were my first avocations? The answer would be, I was (in imagination) a Millwright, whose Water-wheels were composed of Matches. Or a Woodman, converting my chairs into Faggots, and presenting them exultingly to my Parents: (who doubtless caressed the workman more cordially than they approved the work.) Or I was a Stone-digger, presuming to direct my friend the Quarry-man, where to bore his Rocks for blasting. Or a Coach-maker, building Phaetons with veneer stripped from the furniture, and hanging them on springs of Whalebone, borrowed from the hoops of my Grandmother. At another time, I was a Ship Builder, constructing Boats, the sails of which were set to a side-wind by the vane at the mast head; so as to impel the vessel in a given direction, across a given Puddle, without a steersman. In fine, I was a Joiner, making, with one tool, a plane of most diminutive size, the [relative] perfection of which obtained me from my Father’s Carpenter a profusion of tools, and dubbed me an artist, wherever his influence extended. By means like these, I became a tolerable workman in all the mechanical branches, long before the age at which boys are apprenticed to any: not knowing till afterwards, that my good and provident Parent had engaged all his tradesmen to let me work at their respective trades, whenever the more regular engagements of school permitted.
Before I open the list of my intended descriptions, I would crave permission to exhibit two more of the productions of my earliest thought—namely, an Instrument for taking Rats, and a Mouse Trap: subjects with which, fifty years ago, I was vastly taken; but for the appearance of which, here, I would apologize in form, did I not hope the considerations above adduced would justify this short digression. If more apology were needful… Emerson himself describes a Rat-trap: and moreover, defies criticism, in a strain I should be sorry to imitate: my chief desire being to instruct at all events, and to please if I can: without, however, daring to attempt the elegant PROBLEM, stated and resolved in the same words—”Omne tulit punctum, qui miscuitutile dulci.”

We know nothing of White’s education, but he obviously was apprenticed to several trades, because he mentioned: my good and provident Parent had engaged all his tradesmen to let me work at their respective trades.

White says that he brought out one of the first inventions he carried into real practice on coming to manhood about 1782, at the request of the late Doctor Bliss, of Paddington. It was a perpetual wedge machine (first constructed as a crane, see the lower drawing from the book). This was a concentric wheel and axle, the wheel having 100 teeth and the axle one tooth less, thus obtaining a great advantage.

James White's crane from 1782
James White’s crane from 1782

In 1788, giving his address at Holborn London, White took out a British patent No. 1650, for a number of mechanical devices, not all original, e.g. the Chinese windlass is one of them.

In 1792 White modified the inclined disc treadmill-driven crane for wharfs (see the image below) by refinement of having compartments situated on the disc at a leverage proportional to the weight to be lifted. He submitted a model of the crane to the Society of Arts and was rewarded with a premium of 40 guineas or a gold medal.

White's treadmill-driven crane for wharfs from 1792
White’s treadmill-driven crane for wharfs from 1792

At the end of 1792, White departed to Paris, France, where he remained for more than 20 years, making many inventions and starting several business affairs, most of them not very successful.

The first “French” invention of White was a micrometer, based on differential movement. In 1795 White got another patent, this time for a Serpentine boat, i.e. a string of barges, articulated together to reduce traction and for use in restricted waterways, such as canals. In December 1795 White made an association with the Parisian carpenter Jean-Baptiste Decoeur, and the next year they bought a mill at Charenton. Then White invented a “machine à l’instar des lieux à l’anglaise”, patented in 1797.

In 1801 we found James White living at rue de Popincourt, 47, Paris, and working in association with the immigrant Austrian entrepreneur Simon-Thaddée Pobecheim, who established a small cotton mill in the attic of the church Notre-Dame des Blancs-Manteaux. White earned 5% of the profits of the company in exchange for “his talents, processes, and industry in mechanics”. In 1803 White and Pobecheim decided to transfer the company to a former grain mill in Baulne, near Ferté-Alais. In 1804, they took a fifteen-year patent for a “un système préparatoire des matières filamenteuses”, which they perfected several times later, and continued their teamwork until 1807.

At the second Exposition des produits de l’industrie française in 1801, White demonstrated his hypo-cycloidal mechanism, based on the property formulated by the French scientist Philippe de La Hire in 1666, that a point on the circumference of a wheel rolling inside one twice its diameter will describe a straight line. This invention was awarded a renumerating medal by Napoleon Bonaparte. At the same exposition, White presented also a dynamometre.

In the early 1800s, White invented and in 1808 patented single and double helical spur gearing, perhaps the invention on which he seems to have placed most store. He invented also a horizontal water wheel, which was in effect a radial outward-flow turbine.

Another patent, that White took during his stay in France (in 1811) is seemingly of great importance—for the automatic nail-making machine. This was the first machine for making nails from wire, and later considerable manufacture sprang up in France. White has also been credited as being the first to bring out, in 1811, shears for cutting sheet iron in a circular shape.

Hotel Bretonvilliers, Ile de St. Louis, Paris, in 1757
Hotel Bretonvilliers, Ile de St. Louis, Paris, in 1757

After breaking his agreement with Pobecheim in 1807, White moved to rue Saint-Sébastien in Paris, and from 1809 he lived in hotel Bretonvilliers, Ile de St. Louis (still existing, see the nearby painting from 1757), and was engaged in spinning wool mechanics, velvet weaving and nail making.

James White returned to England in February 1815, probably because of the termination of the war by the final defeat of Napoleon at Waterloo. He settled in Manchester presumably because it was one of the foremost world centers of mechanical engineering, and in December 1815, he presented to the Manchester Literary and Philosophical Society the paper On a new system of cog or toothed wheels.

White wrote that “…in 1817 I was employed by Matthew Corbett, one of the proprietors of a factory at the Pin Mill, Ancoats, to erect a number of my wheels,” but owing to the defective lining of the shafting due to overloaded floors, the gears got out of mesh and was scraped out. Later White devised a milling machine to cut the gears by milling cutters.

In 1820 White obtained a British patent No. 4485 for preparation and spinning of textiles.

James White died on 17 December 1825, aged 63, at his home in Chorlton-on-Medlock, Manchester. He was described in his obituary notice as a Civil engineer and author of the New Century of Inventions.